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Balkan Mathematical Olympiads 1984-2006

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Titlu: Balkan Mathematical Olympiads 1984-2006

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Descriere

The present book is a collection of all problems proposed at Balkan Mathematical Olympiads (BMO), also containing some of the problems discussed during these contests by the jury. It is not only a collection of elementary problems but a page of history - the history of BMO, one of the first reginoal mathematical competition for highschool students.

As it is already accepted, International Mathematical Olympiads (IMO), which was created in 1959, had an important contribution to development of mathematical education of young students all around the world. They extended the area of problems used in mathematical education of young people and also improved their quality. Many mathematicians realized how important is to use some parts of their research problems as elementary educational problems.

All problems are presented with complete solutions. Many problems have several alternative solutions and we also present some extensions. The reader can follow the real increasing of the quality of problems as an illustration of the improvement of mathematical preparation of students. An additional preparatory addendum, containing notions and classical useful results has been added to the end of the book.

Cuprins

Preface

Part I Problems and Solutions
The 1st BMO
The 2nd BMO
The 3rd BMO
The 4th BMO
The 5th BMO
The 6th BMO
The 7th BMO
The 8th BMO
The 9th BMO
The 10th BMO
The 11th BMO
The 12th BMO
The 13th BMO
The 14th BMO
The 15th BMO
The 16th BMO
The 17th BMO
The 18th BMO
The 19th BMO
The 20th BMO
The 21st BMO
The 22nd BMO
The 23rdBMO

Part II Supplementary Problems
Geometry
Algebra and Number Theory
Appendix
The Euler Line
The Nine Point Circle
Euler Triangle Formula
Leibniz's Relation
The Einstein Criterion
Young's Inequality

Glossary
Index of notations
References

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